Mentioned in the previous section Zwanzig model [1]} considers a quantum system where somehow initially
prepared a single excited vibrational energy level is coupled with a constant coupling strength (\(C\) ) to the equidistant discrete reservoir
states. In such a formulation (termed in what follows as the bare Zwanzig model) the model allows the exact
analytic solution. We will present below briefly the exact solution (for time evolution of the population for the initial state and reservoir states) found in [2]}, however it is worth to noting first about a possibility of physical realizations of the bare Zwanzig model
assumptions. As an approximate realization one can have in mind the well-known scheme of radiation-less transitions [3]}.
In this experimentally realizable scheme the initially excited state is prepared by a short optical pulse pumping (see Fig.1).
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